Please advise! what kind of training I am lackfor math?

"walala" <mizhael@yahoo.com> wrote in message
news:bven6i$6k6$1@mozo.cc.purdue.edu...
> Dear all,
>
> I have long been headache about this problem... please help me! let me try
> to explain my problem to you:
>
> For years I have been headache about reading math notations. A concept, if
> it is put in straightforward way, I can understand. But if it is put in a
> math notation, or even advanced math notation, I will feel dizzy when I
read
> it. I cannot avoid feeling dizzy if I meet math formulars having more than
3
> lines. But I am in graduate school and must accquaint myself with maths.
For
> some reason, in my research field, information theory and signal
processing,
> if there is no math, the research may be regarded as low quality; hence
high
> quality journals are full of maths. I can never fully understand a paper
> full of maths.
>
> I guess my problem is my lack of exposure to math and lack of systematical
> education in math. I thought I will be a programmer and all my past time
was
> devoted to programming. But later I found programming is kind boring so I
> end up need to use math.
>
> In fact I am quite good in terms of grades in math classes; but I have
only
> studied very few math courses: calculas, linear algebra, complexity
> analysis, probability, all in undergraduate and introductory graduate
level.
>
> So I am at a very akward stage now: if give me undergraduate math to read,
I
> feel too easy and boring, if give me difficult math to read as those in
> Information Theory Transactions, I feel dizzy...
>
> Can anybody recommend some procedures/reference books to give me a
treatment
> for my current sickness? Can anybody give a booklist that any big guy in
the
> field would recommend as a must-read as a systematic treatment to math for
> researchers in math-related engineering/science area?
>
> Thank you very much,
>
> -Walala
>

Dear all,

Thank you all for your warmhearted help! I feel your advice/suggestions are
very helpful, since many of you had already passed succesfully the headache
stage and got your degree!

I guess more specifically what I am asking is how to train myself to
read/understand advanced/complicated/rigorous math to avoid feeling dizzy
when reading math for more than 3 lines and how to think in math and write
rigorous math... something like that... Reading the IEEE transaction on
Information Theory made me very depressed... I wonder why those authors are
so genious that they can invent theorem by theorem, lemma by lemma, ...

Have a great weekend to you all!

-Walala

"Ronald H. Nicholson Jr." <rhn@mauve.rahul.net> wrote in message
news:bvfk32$5r9$1@blue.rahul.net...
> In article <BLOCKSPAMfishfry-0A79E5.17405830012004@netnews.comcast.net>,
> fishfry  <BLOCKSPAMfishfry@your-mailbox.com> wrote:
> >The way to read math is slowly, one line at a time.
>
> Well, everybody works differently, but I would disagree with this.
> One should read the math stuff quickly, but in multiple passes.
>
> On the early passes, try to figure out what notation is being used and
> why, where the math is going, what methods were used and the basic idea
> of how they got to the results.  Hit your textbooks after each step
> if you find a particular notation, assumption or method too opaque.
> Perhaps look into some of the citations to see if they explain some of
> the concepts better.  Then, after thinking about the stuff for awhile,
> and maybe writing out some of equations in your own formulations, the
> later passes won't be nearly as slow or frustrating.
>
> I remember checking a book out of the library to read about some DSP
> topic.  The chapters on that topic were completely unreadable, so I'd
> turn the book back in to the library and check out a different book.
> Finally after trying 4 or 5 different unreadable books in succession,
> there were no other books on the subject to be found.  So I went back
> to the first book I had tried, and found that the words and equations
> must have rearranged themselves on the pages while the book was sitting
> on the library shelf, because the chapter of interest was now completely
> readable.
>
>
> IMHO. YMMV.
> -- 
> Ron Nicholson   rhn AT nicholson DOT com   http://www.nicholson.com/rhn/
> #include <canonical.disclaimer>        // only my own opinions, etc.

Hi Ron,

That's an interesting experience. That happened to me too. Sometimes after
turnning around several books, the original one is now easier to
understand...

-Walala

"Bob Cain" <arcane@arcanemethods.com> wrote in message
news:401B5752.F096FF34@arcanemethods.com...
>
>
> Fred Marshall wrote:
> >
> > I must say that your problem is very familiar to me too!  So don't be
> > disheartened.
>
> Me too.  Early on, math came with great difficulty to me
> also and being in an electrical engineering program I was
> constantly challenged.  It takes perserverence but the
> facility comes with usage.  I am amazed today at how easily
> I can move into a new mathematical area and how quickly it
> makes sense.  I'da never thought.  :-)

Great! Which courses/books you feel are most important in your pathway to
become a master of maths?

-Walala

"Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message
news:oamdnddLba-V3YbdRVn-uw@centurytel.net...
> until someone tells you they're really important.

Then I will lost the chance to identify a promising emerging discovery, etc.
right?

> You will never read
> *everything* anyway - so you may as well be selective.  And, by this I
mean
> you will never read everything in either: information theory, in circuit
> theory, in DSP, in control systems because each topic is just too broad
and
> has too many articles.
>
> Hint:  look for the referenced articles.  Note that the "classic" papers
are
> mostly much easier to read than others.  Put your time into the classics
and
> into the more recent ones that are being often referenced.  Then pick a
> single topic and research it very well - using the widest variety of
search
> methods possible - including Scientific Abstracts if that's still around.
A
> careful review of the papers on that one narrow subject will reveal papers
> in categories something like this:
>
> - the classics
> - a much better notion of what the often-used references are - which
should
> become part of your research base.
> - some very interesting ideas that you haven't seen before
> - quite a few papers that aren't very clear and don't seem to mean much in
> context of your research - they are off-topic
> - some interesting "facts" and proofs that may come in handy in your
> research of this topic.
>

This is good.

>
>
> Now, if you want references, then in what area?  You need to help focus
the
> helpers too!
>

As I mentioned earlier, I am hoping to have a (short) list of
courses/books/online resources that once I finish them, I can promise myself
I won't feel dizzy reading these papers, as Bob mentioned in his post: he
now feels very easily to get into a new math field...  this gives me a lot
hope... The field is about general or specific math that are helpful signal
proceesing, image processing, communications, etc.

Thank you!

-Walala

"Bob Cain" <arcane@arcanemethods.com> wrote in message
news:401C9CAB.FA5E6CE8@arcanemethods.com...
>
>
> Fred Marshall wrote:
> >
>
> I'm looking at one such now:
>
>   http://www.atvs.diac.upm.es/publicaciones/docs/Bot00a.pdf
>

Hi Bob,

I have got the feeling that 4 page paper can just tell me what the authors
have done and it leaves me to journal paper to fully understand the author's
method most of the time. I don't the other people have the same feeling as I
do...

-Walala

walala wrote:
> 
> Great! Which courses/books you feel are most important in your pathway to
> become a master of maths?

I didn't say I had mastery, just perserverence.  :-)  

I wish I could answer your question but after the E.E.
education (which was the tip of the iceberg) my learning has
been pretty much a pseudo random sequence.  I have only
known one completely self taught mathematician in many years
of work so I honestly would recommend taking a program of
education.  Personally I think that electrical engineering
crams the most useful math and takes the most pragmatic
attack on it.  When I was taking it 40 years ago the formal
math classes were pretty much limited to analytic geometry,
calculus and differential equations.  Everything else was
learned in the courses that needed their application.  I
think that approach is the best for an applied mathematician
because it is a model of how you will extend that education
on your own and gets you used to doing it.


Bob
-- 

"Things should be described as simply as possible, but no
simpler."

                                             A. Einstein

walala wrote:
> 
> 
> You said it. After reading your experience, I now more positively think that
> real analysis should be able to cure my sickness. I heard it many times, but
> was not very sure that I should select this one to take out of those many
> math courses... Thank you!
> 

Yes. Yes. Yes, although I'm not sure about the "real" part. 
I hope that in the future all courses dealing with
transforms will use that basis.  <puns intended>


Bob
-- 

"Things should be described as simply as possible, but no
simpler."

                                             A. Einstein

Mizwalala:

How many languages do you know? Learning standard math notation is somewhat
like learning a second language--it takes some practice with it before you
immediately understand the meaning, without having to look up the
syntax/notation. I don't recall that the syntax got any different or harder
from undergraduate to graduate level, but the reliance on the understanding
of the math without giving practical examples became much greater.

Or, if you are familiar with the notation, then perhaps the ideas in the
journals are really a bit complex for you. Don't take it the wrong way--it
would not mean your IQ is small, it would only mean that you are more geared
to practical thinking than abstract. Read as, your interests lie more in the
applications than the abstract. It would make you a fine engineer, but would
create problems if you would pursue a career in academia.

On the flip side, I have worked with many people who left academia to chase
gold in startups, but their thinking was way to bent on the abstract to ever
help generate anything useful or money-making. They became high profile
drains on the payroll. Not all, but some.

Regarding your master's (or PhD), I'm sure you can do a fine thesis that is
application oriented rather than theoretical. As has been stated in this
newsgroup before, practical applications are somewhat lacking in
professional journals. Make something really cool work for a company funding
the research, and I'm sure your advisor won't care about publishing. If no
one is funding the research, you have a problem, as then you become another
feather in the hat of your advisor's publishing record (MHO only).

Jim


"walala" <mizhael@yahoo.com> wrote in message
news:bven6i$6k6$1@mozo.cc.purdue.edu...
> Dear all,
>
> I have long been headache about this problem... please help me! let me try
> to explain my problem to you:
>
> For years I have been headache about reading math notations. A concept, if
> it is put in straightforward way, I can understand. But if it is put in a
> math notation, or even advanced math notation, I will feel dizzy when I
read
> it. I cannot avoid feeling dizzy if I meet math formulars having more than
3
> lines. But I am in graduate school and must accquaint myself with maths.
For
> some reason, in my research field, information theory and signal
processing,
> if there is no math, the research may be regarded as low quality; hence
high
> quality journals are full of maths. I can never fully understand a paper
> full of maths.
>
> I guess my problem is my lack of exposure to math and lack of systematical
> education in math. I thought I will be a programmer and all my past time
was
> devoted to programming. But later I found programming is kind boring so I
> end up need to use math.
>
> In fact I am quite good in terms of grades in math classes; but I have
only
> studied very few math courses: calculas, linear algebra, complexity
> analysis, probability, all in undergraduate and introductory graduate
level.
>
> So I am at a very akward stage now: if give me undergraduate math to read,
I
> feel too easy and boring, if give me difficult math to read as those in
> Information Theory Transactions, I feel dizzy...
>
> Can anybody recommend some procedures/reference books to give me a
treatment
> for my current sickness? Can anybody give a booklist that any big guy in
the
> field would recommend as a must-read as a systematic treatment to math for
> researchers in math-related engineering/science area?
>
> Thank you very much,
>
> -Walala
>
>

"Bob Cain" <arcane@arcanemethods.com> wrote in message
news:401C9CAB.FA5E6CE8@arcanemethods.com...
>
>
> Fred Marshall wrote:
> >
> > > On the other hand, much of my learning was in puzzling
> > > through exactly such papers and filling in the gaps in them
> > > and in my own knowledge to come to an understanding of the
> > > topic that was sufficient for implementation or variation.
> > > I'd say don't skip a paper that you feel you should be able
> > > to understand but don't.  Rather, buckle down and work it
> > > through.  I can think of some papers that I spent months
> > > coming back to, setting aside, looking at things that might
> > > clarify them until the final aha moment that made it all
> > > worth it.
> >
> > I think we agree.  My point was in being choosy about which papers to
spend
> > time on.
>
> For sure.  I'm just recommending that obscurity not be a
> criterion in and of itself.  It can be difficult to
> anticipate that there may be a nugget at the end of the
> trail but one develops a sense of it.
>
> I'm looking at one such now:
>
>   http://www.atvs.diac.upm.es/publicaciones/docs/Bot00a.pdf
>
> I've got some serious work to do to know whether this
> contains an answer to my current problem but my sense is
> that it does.  The question now is whether it may be too
> concise in its discussion of the noise reduction part of the
> approach that I won't be able to use it even when I've
> accumulated the background.  I know several authors that go
> to pains to develop a formulation of the problem to then
> just tell you that they've solved it.  :-)

Bob,

Without reading it, the paper seems pretty straight in terms of notation.
It even has block diagrams!  Not the sort I was thinking of.  I mean the
kind with pages of matrix equations that you just *know* will take many
hours to figure out what they're talking about and then wonder if it's all
smoke and no fire!

Fred

Bob Cain <arcane@arcanemethods.com> wrote in message news:<401D5FFB.EE2DFD91@arcanemethods.com>...
> walala wrote:
> > 
> > 
> > You said it. After reading your experience, I now more positively think that
> > real analysis should be able to cure my sickness. I heard it many times, but
> > was not very sure that I should select this one to take out of those many
> > math courses... Thank you!
> > 
> 
> Yes. Yes. Yes, although I'm not sure about the "real" part. 
> I hope that in the future all courses dealing with
> transforms will use that basis.  <puns intended>

Well, real analysis could get real enough. I have been involved in 
discussions of two real-world data processing problems where the cause 
of the prblem could be traced back to concepts I knew from real analysis.

In both cases there were systems up and running, making measurements 
and doing processing but the processed measurements were nowhere 
near the "known" answeres. In one case people didn't understand what I 
was talking about and proceeded in 40 year old tracks, with little if 
any progress in either explaining the cause or correcting the problem. 

In the other case, it appears that people understand the basic nature 
of the practical (if not theoretical) predictions and are aware of 
what to look for. They have designed a series of experiments to 
investigate where and why the failiure occurs. The fun part is that I, 
based on Real Analysis and concepts from Sturm-Liouville theory, am able 
to make predictions where in that test series the failiure will occur 
and why. I have really put my neck on the line, as I have pointed out
one particular step in the experiment series where I believe the 
processing problems will be seen.  

Just a digression: Last week I was a bit euphoric about making my own 
MPEG videos. It appears that the videos made all the difference. After 
having showed the video, it was very easy to discuss the nature of the 
measurement situation and what would cause problems in measurements 
and data processing. I believe it was well worth the effort.

Rune